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The conjugate prior distribution of a categorical distribution is a Dirichlet distribution. [2] See the section below for more discussion. The sufficient statistic from n independent observations is the set of counts (or, equivalently, proportion) of observations in each category, where the total number of trials (=n) is fixed.
The Irwin–Hall distribution is the distribution of the sum of n independent random variables, each of which having the uniform distribution on [0,1]. The Bates distribution is the distribution of the mean of n independent random variables, each of which having the uniform distribution on [0,1]. The logit-normal distribution on (0,1).
When k is bigger than 2 and n is 1, it is the categorical distribution. The term "multinoulli" is sometimes used for the categorical distribution to emphasize this four-way relationship (so n determines the suffix, and k the prefix). The Bernoulli distribution models the outcome of a single Bernoulli trial.
The categorical distribution is the generalization of the Bernoulli distribution for variables with any constant number of discrete values. The Beta distribution is the conjugate prior of the Bernoulli distribution. [5] The geometric distribution models the number of independent and identical Bernoulli trials needed to get one success.
The probability distribution associated with a random categorical variable is called a categorical distribution. Categorical data is the statistical data type consisting of categorical variables or of data that has been converted into that form, for example as grouped data.
This is a list of statistical procedures which can be used for the analysis of categorical data, also known as data on the nominal scale and as categorical variables. General tests [ edit ]
In the same way as the Dirichlet distribution is the conjugate prior for the categorical distribution, the Dirichlet process is the conjugate prior for infinite, nonparametric discrete distributions. A particularly important application of Dirichlet processes is as a prior probability distribution in infinite mixture models.
In mathematics, the term categorical probability denotes a collection of category-theoretic approaches to probability theory and related fields such as statistics, ...